A space-time network is used to model traffic flows over time for a capacitated road transportation system having one-way and two-way streets. Also traffic signal lights, which change the network structure, are explicitly incorporated into the model. A linear (time) cost per unit flow is associated with each arc, and it is shown that under the model structure, travel time on a street is piecewise linear convex function of the number of units travelling on that street. Hence congestion effects are explicitly considered while maintaining the linear nature of the model. Two efficient solutions methods are proposed. A network flow solution for multiple source single destination network and a shortest path solution for a single source single destination network